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Motion in a Plane — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane4 Marks
Question
Explain the terms:
$i$. Average velocity
$ii$. Instantaneous velocity
$iii$. Average speed
$iv$. Instantaneous speed
✓

Answer

$(i)$ Average velocity:
$1$. Average velocity $( \overrightarrow{ v }_{ av } )$ of an object is the displacement $( \Delta \overrightarrow{ x } )$ of the object during the time interval $(\Delta t)$ over which average velocity is being calculated, divided by that time interval.
$2. $ Average velocity $=\left(\frac{\text { Displacement }}{\text { Time interval }}\right)$
$\overrightarrow{ V _{ av }}=\frac{\overrightarrow{ x }_2-\overrightarrow{ x }_1}{ t _2- t _1}=\frac{\Delta \overrightarrow{ x }}{\Delta t }$
$3$. Average velocity is a vector quantity.
$4$. Its $SI$ unit is $m / s$ and dimensions are $\left[ M ^0 L^1 T^{-1}\right]$
$5$. For example, if the positions of an object are $x+4 m$ and $x = +6 m$ at times $t = O$ and $t =1$ minute respectively, the magnitude of its average velocity during that time is $V _{ av }=(6$ -4) $1(1-0)=2 m$ per minute and its direction will be along the positive $X$-axis.
$\therefore \overrightarrow{ v }_{ av }=2$ im $/ \min$
Where, $i =$ unit vector along $X -$ axis.
$(ii)$ Instantaneous velocity:
$1$. The instantaneous velocity $(\vec{V})$ is the limiting value of $;$ he average velocity of the object over a small time interval $(\Delta t)$ around $t$ when the value of lime interval goes to zero.
$2$. It is the velocity of an object at a given instant of time.
$3$. $\vec{v}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \overrightarrow{ x }}{\Delta t }=\frac{ d \overrightarrow{ x }}{ dt }$ where $\frac{d \vec{x}}{d t}$ derivative of $\vec{x}$ with respect to $t$.
$(iii)$ Average speed:
$1$. Average speed of an object is the total path length $($distance$)$ travelled by the object during the time interval over which average speed is being calculated, divided by that time interval.
$2$. Average speed $=\frac{\text { Total path length }}{\text { Total time interval }}$
$3$. Average speed is a scalar quantity.
$4$. Its $S.I$. unit is $m / s$ and dimensions are $\left[ M ^0 V^1 T^{-1}\right]$.
$5$. In rectilinear motion;
$•$ If the motion of the object is only in one direction, then the magnitude of displacement will be equal to the path length and hence the magnitude of average velocity will be equal to the average speed.
$•$ If the motion of the object reverses its direction, then the magnitude of displacement will be less then the path length and hence the magnitude of average velocity will be less than the average speed.
$(iv)$ Instantaneous speed:
The instantaneous speed is the limiting value of the average speed of the object over a small time interval $‘\triangle t\ ’$ around t when the value of time interval goes to zero.

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